Can installed scripts cause conflicts with each other?
Yes, two add-ons defining the same operator will “conflict” - in that the latest registering one will override any previous registration. The same goes for other registrable classes (panels, menus, UILists, etc.).

Note that add-ons can even override Blender's own operators, menus etc. that way (though this is totally not recommended).

Prefixing classes' IDs with something related to your add-on is the best way to go.